An efficient adaptive rescaling scheme for computing Hele-Shaw problems

Abstract eng:
In this paper, we present an efficient rescaling scheme for computing moving interface problems. The idea is to design an adaptive time—space mapping such that in the new time scale, the interfaces can evolve logarithmic fast for small—sized interface at early stage of growth and exponentially fast for large—sized interface at later times. During the evolution, the new spatial scale guarantees the conservation of the area/volume enclosed by the interface. Comparing with the original rescaling idea in [3], this adaptive scheme dramatically improves the slow growth at early times when the interface size is small. Our results show that the original three—week computation in [3] can be done in just four days using the adaptive scheme.

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